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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 29645d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29645.h4 | 29645d1 | \([1, -1, 0, -217520, 52598475]\) | \(-5461074081/2562175\) | \(-534014611704533575\) | \([2]\) | \(368640\) | \(2.1077\) | \(\Gamma_0(N)\)-optimal |
| 29645.h3 | 29645d2 | \([1, -1, 0, -3804565, 2856950256]\) | \(29220958012401/3705625\) | \(772335182217300625\) | \([2, 2]\) | \(737280\) | \(2.4542\) | |
| 29645.h2 | 29645d3 | \([1, -1, 0, -4130660, 2338524425]\) | \(37397086385121/10316796875\) | \(2150251359582257421875\) | \([2]\) | \(1474560\) | \(2.8008\) | |
| 29645.h1 | 29645d4 | \([1, -1, 0, -60871190, 182810845531]\) | \(119678115308998401/1925\) | \(401213081671325\) | \([2]\) | \(1474560\) | \(2.8008\) |
Rank
sage: E.rank()
The elliptic curves in class 29645d have rank \(1\).
Complex multiplication
The elliptic curves in class 29645d do not have complex multiplication.Modular form 29645.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
